一类分数阶非线性混沌系统的同步控制  

Synchronization Control for a Class of Fractional Order Nonlinear Chaotic Systems

作　　者：邵书义[1,2] 陈谋[1,2] 

机构地区：[1]南京航空航天大学江苏省物联网与控制技术重点实验室,江苏南京210016 [2]南京航空航天大学自动化学院,江苏南京210016

出　　处：《计算机仿真》2015年第4期394-398,共5页Computer Simulation

基　　金：江苏省六大高峰人才项目(2012-XXRJ-010);航空科学基金(20145152029)

摘　　要：在分数阶非线性系统同步控制的研究中,针对一类分数阶非线性混沌系统,研究了基于分数阶控制器的同步方法。利用状态反馈方法和分数阶微积分定义,设计了分数阶混沌系统同步控制器。进一步,根据分数阶非线性系统稳定性理论、Mittag-Leffler函数、Laplace变换以及Gronwall不等式,证明了同步控制器的有效性。最后,通过数值仿真,实现了初始值不同的两个分数阶非线性混沌系统同步。误差响应曲线表明研究的分数阶非线性系统同步响应速度快,控制精度高,验证了本文所设计的混沌同步控制方案的可行性。In this paper, on the basic of the fractional order controller, a synchronization control scheme is studied for a class of fractional order nonlinear chaotic systems. According to the state - feedback method and the definition of fractional calculus, a fractional order synchronization controller is designed. By using the stability analysis theorems of fractional order nonlinear systems, Mittag - Leffler function, Laplace transform and the Gronwall inequality, the effectiveness is proven of synchronization controller. Finally, under the designed synchronization controller, the synchronization is realized between two fractional order nonlinear chaotic systems with different initial conditions. Error response curves show the fast response and high control precision of synchronization for fractional order nonlinear systems. Numerical simulations further illustrate the feasibility of the proposed synchronization control scheme.

关 键 词：分数阶非线性系统 分数阶控制器 混沌 同步控制 

分 类 号：TP391.9[自动化与计算机技术—计算机应用技术]